Characterization of the geometric and exponential random variables

Artikel i vetenskaplig tidskrift, 2004

Let the random variable X be distributed over the non-negative integers and let Lm and Rm be the quotient and the remainder in the division of X by m. It is shown that X is geometric if and only if Lm and Rm are independent for m=2,3, . . . . In similar terms is also characterized the exponential random variable.